Study of Pegloticase (KRYSTEXXA®) Plus Methotrexate in Patients With Uncontrolled Gout

Inclusion Criteria: 1. Willing and able to give informed consent. 2. Willing and able to comply with the prescribed treatment protocol and evaluations for the duration of the study. 3. Adult men or women ≥18 to ≤65 years of age. 4. Women of childbearing potential (including those with an onset of menopause \<2 years prior to screening, non-therapy-induced amenorrhea for \<12 months prior to screening, or not surgically sterile \[absence of ovaries and/or uterus\]) must have negative serum/urine pregnancy tests during the Screening/(methotrexate) MTX Run in Period; participants must agree to use 2 reliable forms of contraception during the study, one of which is recommended to be hormonal, such as an oral contraceptive. Hormonal contraception must be started ≥1 full cycle prior to Week -4 (start of MTX dosing) and continue for 30 days after the last dose of pegloticase or at least one ovulatory cycle after the last dose of MTX (whichever is the longest duration after the last dose of pegloticase or MTX). Highly effective contraceptive methods (with a failure rate \<1% per year), when used consistently and correctly, include implants, injectables, combined oral contraceptives, some intrauterine devices, sexual abstinence, or vasectomized partner. 5. Men who are not vasectomized must not impregnant their female partner during the study and for at least 3 months after the last dose of MTX. 6. Hyperuricemia at the Screening, Week -4, or Week -2 Visit of the Screening/MTX Run in Period, as documented by sUA ≥6 mg/dL. 7. Uncontrolled gout, defined as meeting the following criteria: serum uric acid (sUA) ≥6 mg/dL prior to entry into the pegloticase +IMM Period (any laboratory tests during screening up to and including during the MTX Run in Period) and at least 1 of the following: inability to maintain sUA \<6 mg/dL on other urate-lowering therapy; intolerable side effects associated with current urate-lowering therapy; functionally limiting tophaceous deposits (including those detected clinically or by dual-energy computed tomography \[DECT\] imaging) 8. Able to tolerate MTX 15 mg for 4 weeks during the MTX Run-in Period prior to the first dose of pegloticase. Exclusion Criteria: 1. Weight \>160 kg (352 pounds). 2. Any serious acute bacterial infection, unless treated and completely resolved with antibiotics at least 2 weeks prior to the Week -4 Visit of the MTX Run-in Period. 3. Severe chronic or recurrent bacterial infections, such as recurrent pneumonia or chronic bronchiectasis. 4. Current immunocompromised condition, including current or chronic treatment with systemic immunosuppressive agents, including prednisone \>10 mg/day or equivalent dose of other corticosteroid. 5. History of any transplant surgery requiring maintenance immunosuppressive therapy. 6. Known history of hepatitis B virus surface antigen positivity or hepatitis B DNA positivity. 7. Known history of hepatitis C virus RNA positivity. 8. Human immunodeficiency virus (HIV) positivity (tested at the Screening Visit). 9. Glucose-6-phosphate dehydrogenase (G6PD) deficiency (tested at the Screening Visit). 10. Severe chronic renal impairment (glomerular filtration rate \<25 mL/min/1.73 m\^2) or currently on dialysis. 11. Non-compensated congestive heart failure or hospitalization for congestive heart failure within 3 months of the Screening Visit, uncontrolled arrhythmia, treatment for acute coronary syndrome (myocardial infarction or unstable angina), or uncontrolled blood pressure (\>160/100 mmHg) at the end of the Screening/MTX Run-in Period. 12. Pregnant, planning to become pregnant, breastfeeding, planning to impregnant female partner, or not on an effective form of birth control, as determined by the Investigator. 13. Prior treatment with pegloticase (KRYSTEXXA®), another recombinant uricase (rasburicase), or concomitant therapy with a polyethylene glycol-conjugated drug. 14. Known allergy to pegylated products or history of anaphylactic reaction to a recombinant protein or porcine product. 15. Contraindication to MTX treatment or MTX treatment considered inappropriate. 16. Known intolerance to MTX. 17. Receipt of an investigational drug within 4 weeks or 5 half-lives, whichever is longer, prior to MTX administration at Week -4 or plans to take an investigational drug during the study. 18. Current liver disease, as determined by alanine transaminase or aspartate transaminase levels \>3 times upper limit of normal at the Screening Visit. 19. Currently receiving systemic or radiologic treatment for ongoing cancer, excluding non melanoma skin cancer. 20. History of malignancy within 5 years other than non-melanoma skin cancer or in situ carcinoma of cervix. 21. Uncontrolled hyperglycemia with a plasma glucose value \>240 mg/dL at screening that is not subsequently controlled by the end of the Screening/MTX Run-in Period. 22. Diagnosis of osteomyelitis. 23. Known history of hypoxanthine-guanine phosphoribosyl-transferase deficiency, such as Lesch-Nyhan and Kelley-Seegmiller syndrome. 24. Unsuitable candidate for the study, based on the opinion of the Investigator (e.g., cognitive impairment), such that participation might create undue risk to the participant or interfere with the participant's ability to comply with the protocol requirements or complete the study. 25. Alcohol use in excess of 3 alcoholic beverages per week. 26. Currently receiving allopurinol and unable to discontinue medication 7 days prior to MTX dosing at Week -4 and unable to discontinue treatment during the duration of the study.